Problem Solving

What's the difference between x/y>1 and x>y?
I thought the answer was " no difference"
But, according to GMAT Prep, there is a difference.
In x/y>1, both x & y have to be + or -.
But there is no such criteria in x>y.
I am still not convinced.
Do help!!

Regards,
mukherjee

x/y > 1 & x > y

For x/y > 1 .. both "x" & "y" should have same sign ..

For example:
x=-5 & y=-3 ===> (-5)/(-3) = 1.xx

For x > y.. there is no such criteria.. both X & y can have same sign or different sign

For example:
x=-3 & y=-5 ===> -3 > -5
x=+3 & y=-5 ===> +3 > -5

[email protected] wrote:What's the difference between x/y>1 and x>y?
I thought the answer was " no difference"
But, according to GMAT Prep, there is a difference.
In x/y>1, both x & y have to be + or -.
But there is no such criteria in x>y.
I am still not convinced.
Do help!!

Regards,
mukherjee

When we multiply each side of an inequality by a NEGATIVE value, we must FLIP the direction of the inequality.

If x/y > 1 and y<0, then multiplying each side by y -- a negative value -- requires that we FLIP > to <:
x/y > 1
y * x/y < y * 1
x < y.
Since y<0, the following relationship is implied:
x < y < 0.
Examples for x and y:
x = -2 and y = -1, with the result that x/y = -2/-1 = 2.
x = -10 and y = -2, with the result that x/y = -10/-2 = 5.
And so on.

If x/y > 1 and y>0, then multiplying each side by y -- a positive value -- does NOT affect the direction of the inequality:
x/y > 1
y * x/y > y * 1
x > y.
Since y>0, the following relationship is implied:
x > y > 0.
Examples for x and y:
x = 2 and y = 1, with the result that x/y = 2/1 = 2.
x = 10 and y = 2, with the result that x/y = 10/2 = 5.
And so on.

Thus, x/y > 1 does NOT imply that x>y.
Rather, x/y > 1 implies that EITHER x>y>0 OR that x<y<0.

Great Explanation!

Regards,
Mukherjee

[email protected] wrote:What's the difference between x/y>1 and x>y?

Plug in some values -

Let x = +3 and y = +2

x/y = 3/2 =1.5 >1


Let x = -3 and y = -2

x/y = (-3) / (-2 ) = 3/2 = 1.5 >1


However if You take one +ve and one -ve value the whole thing collapses -

Let x = -3 and y = +2

x/y = (-3) / (2 ) = -3/2 = -1.5 < 1

Again ,

Let x = 3 and y = -2

x/y = (3) / (-2 ) = 3/-2 = -1.5 < 1



Hence both x & y have to be either + or -.